Godoy, G., Tiwari, A. (2009). Invariant Checking for Programs with Procedure Calls. In: Palsberg, J., Su, Z. (eds) Static Analysis. SAS 2009. Lecture Notes in Computer Science, vol 5673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03237-0_22
Invariants are a crucial component of the overall correctness of programs. We explore the theoretical limits for doing automatic invariant checking and show that invariant checking is decidable for a large class of programs that includes some recursive programs. The proof uses known results like the decidability of Presburger arithmetic and the semilinearity of the Parikh image of a regular language. Removing some of the restrictions on the program model leads to undecidability of the invariant checking problem.
Keywords: Program Model, Basic Block, Regular Language, Procedure Call, Recursive Program